Bulbasaur/Fushigitane is the only Pokemon of his that overtly refused to evolve. Squirtle, Totodile, etc. never showed a desire to avoid evolution. Chalk it up to the anime making a mess of in-game level mechanics
I doubt Charizard would've been able to help Ash win the Kanto League either way. Richie got stomped by his next opponent and said opponent had a Rock/Ground Pokemon like Rhydon at his disposal (giving it a massive advantage over Ash's Charizard), not to mention in the next two rounds after that the competition could have only grown tougher and tougher. It's also worth noting that Charizard lost against a Hoenn guy's Blaziken despite the fact that he'd only been through two regions (less than Ash who'd been through Johto and Kanto as well as the Orange Islands), plus Ash's team was the strongest it'd ever been in Hoenn (overall, although I don't know if any of them were stronger than Lizardon individually) and it still only made it to Top 8 in that region. The first time Ash was ever in a good position to win a regional league without Uberfags blocking his way would be in Sinnoh I think. In any other league before, he'd have at most made it to the finals before losing to the eventual champion. Plus, even Paul/Shinji lost 3 leagues before he went to Sinnoh and he was a more skilled trainer than Ash when they met
even if part of that can be credited to Ash's skill resetting between regions.